Weird! I don't think I've ever seen anything like that in the US. Airline employees will often check passports and visas and such, but only to make sure you're actually allowed to enter the country they're taking you to. (The airline has to pay to fly you back if you get refused entry, so they want to make sure to catch such people early!)

Not casting doubt on what you say, I just haven't seen this myself. I've never flown internationally out of LAX. Only domestically once, and I hope it will be my last!

Most likely fly on round trip tickets, in which case the return flight was already paid for.

But they'd have to fly back early, which is an additional expense for the airline, at least potentially. Also I think they might be fined by the authorities too.